Using the dimension reduction procedure, a one-dimensional model of a periodic blood flow in the artery through a small hole in a thin elastic wall to a spindle-shaped hematoma, is constructed. This model is described by a system of two parabolic and one hyperbolic equations provided with mixed boundary and periodicity conditions. The blood exchange between the artery and the hematoma is expressed by the Kirchhoff transmission conditions. Despite the simplicity, the constructed model allows us to describe the damping of a pulsating blood flow by the hematoma and to determine the condition of its growth. In medicine, the biological object considered is called a false aneurysm.